Write the value of n for which nth of the A.P.s 3, 10, 17, ... and 63, 65, 67, ... are equal.

Let n^th term of A.P. 3,10,17,… be a_n

And n^th term of A.P. 63,65,67,…be a^’_n

So,a₁₌3 and a₂=10

∴ d=a₂-a₁=10-3=7

And, a₁’=63 and a₂’=65

∴ d’=a₂’-a₁’=65-63=2

Now, a_n=a₁+(n-1)d

=3+(n-1)7

=3+7n-7

=7n-4

And, a_n’=a₁’+(n-1)d’

=63+(n-1)2

=63+2n-2

=2n+61

Now,it is given that a_n=a_n’

∴ 7n-4=2n+61

∴ 7n-2n=61+4

∴ 5n=65

∴ n=13